Nonlinear vector multiresolution analysis

We explore the use of multiresolution analysis for vector signals, such as multispectral images or stock market portfolio time series. These signals often contain local correlations among components that are overlooked in a component-by-component analysis. We show that a coarse signal defined by taking local arithmetic averages is equivalent to analyzing the signal component by component, but by using the average that minimizes the L/sup 2/ distance to the local points results in a non-separable vector multiresolution analysis. We propose using the vector multiresolution representation for signal processing tasks such as compression and denoising. We prove some results in denoising and present color image examples.